As if someone can't be racist because they belong to a particular group. (Anyone can be racist, it's not limited to one group. Acting like it can be is nonsense.)
This is factually incorrect. I'll explain this as simply as I can, because this is a common myth that needs to be debunked.
Racism, and other -isms, are acts of oppression. Oppression requires two things: discrimination and power. Many people often think of racism, sexism, etc. as just discrimination based on race, sex, and so on. No. That is just simply called discrimination. By that, you are right - a black person can discriminate against a white person, a woman can discriminate against a man, but that doesn't make those racism or sexism respectively. It just makes them acts of discrimination.
Looking at the power component more closely, let me explain what that means. In order for it to be considered oppression, and therefore racism/sexism/etc., there must be a dominant power dynamic at play. So, because a white man has privilege that a black woman does not, their acts of discrimination would be considered racism/sexism (depending on what it is). Privilege, as a side note, does not mean that the white man in this example is better off than the specific black woman. It just means the white man does not experience the same systemic barriers and obstacles as someone who is black and/or a woman. Furthermore, in this example we are also seeing
intersectionality because the black woman has too marginalized identities that are intertwined and make the racism and sexism she experiences that much worse than say, what a white woman or black man would experience (because both of those people have some privilege that the black woman does not.
A real-time example of this is a woman saying to a man "man up" or "be a man." This is wrong and problematic. But it isn't sexism. Sexism would be the man saying something like "stay in the kitchen" to the woman. This, however, is just a case of discrimination and bias. It is an issue that needs to be addressed, and men shouldn't be forced into a stereotype of "manliness" but it doesn't qualify as sexism or oppression. It does, however, perpetuate gender norms and gender roles, which further oppresses women into an inferior role in society. And that perpetuates and allows sexism to continue to exist. By saying man up, the woman contributed to a sexist society and allowed for it to continue to be accepted, but did not directly commit an act of sexism herself.
Reverse racism is not a thing. It's either racism (when discrimination and power are both present) or it isn't.